nLab Author — Thomas Holder

Overview

Thomas Holder has contributed to 466 nLab pages.

Most recent contributions

All pages contributed to

• (0,1)-topos
• (dense,closed)-factorization
• (geometric surjection, embedding) factorization system
• 2-category
• abductive reasoning
• absolute conclusion
• abstract model theory
• accessible category
• Adj
• adjoint functor theorem
• adjoint lifting theorem
• adjoint modality
• adjoint triangle theorem
• affine space
• Albrecht Dold
• Alfred Tarski
• algebraic curve
• amalgamation property
• amazing right adjoint
• Anders Kock
• antithesis interpretation
• arithmetic pretopos
• Artin gluing
• atomic geometric morphism
• atomic site
• atomic topos
• Attempt to Introduce the Concept of Negative Quantities into Philosophy
• Aufhebung
• axiom of choice
• axiom of infinity
• axiom of replacement
• bagdomain topos
• Barr's theorem
• Bas van Fraassen
• Beth definability theorem
• BHK interpretation
• bi-Heyting topos
• bicategory of fractions
• bifibration
• big and little toposes
• binary Golay code
• binary linear code
• bipartite graph
• bireflective subcategory
• bitopological space
• Boolean topos
• Boone conjecture
• bornological set
• bornological topos
• boundary
• Bourbaki
• braid group
• Brauer group
• Burali-Forti's paradox
• Burnside ring
• calculus of constructions
• canonical formula of myth
• Cantor-Schroeder-Bernstein theorem
• cartesian logic
• cartesian theory > history
• categorial grammar
• categorical compositional distributional semantics
• category of elements
• category of fractions
• category of presheaves
• category theory
• Category Theory conference
• Cauchy complete category
• center
• Chevalley's theorem on constructible sets
• choice object
• Clara Löh
• classifying topos
• classifying topos for the theory of objects
• Claude Chevalley
• Claude Lévi-Strauss
• closed subspace
• closed subtopos
• co-Heyting algebra
• co-Heyting boundary
• co-Heyting negation
• coalgebra of the real interval
• codensity monad
• coding theory
• coherent logic
• cohesive topos
• Cohesive Toposes -- Combinatorial and Infinitesimal Cases
• Cohesive Toposes and Cantor's "lauter Einsen"
• Cole's theory of spectrum
• combinatory logic
• compact-open topology
• compactly generated topological space
• compactness theorem
• complete small category
• complete theory
• completely distributive lattice
• completion
• compositionality
• comprehensive factorization system
• Comptes rendus hebdomadaires des séances de l'Académie des sciences
• conceptual completeness
• conservative functor
• Constanze Roitzheim
• construction in philosophy
• context-sensitive grammar
• continuous category
• continuous poset
• continuum hypothesis
• cosheaf
• Craig interpolation theorem
• Critique of Pure Reason
• crossed group
• crossed homomorphism
• crystalline site
• cubical set
• cumulative hierarchy
• curve
• cyclic category
• cyclic set
• De Morgan Heyting algebra
• De Morgan topos
• De Morganization
• decidable object
• Deligne completeness theorem
• Deligne-Mumford stack
• dense functor
• dense sub-site
• dense subcategory
• dense subspace
• dense subtopos
• dense topology
• dependent type theoretic methods in natural language semantics
• Diaconescu's theorem
• diagonal argument
• Dieter Puppe
• differential cohesive (infinity,1)-topos
• difunctional relation
• disjoint coproduct
• disjunctive logic
• distributive category
• Dold-Kan correspondence
• Dold-Thom theorem
• dominant geometric morphism
• Dorette Pronk
• double negation
• dualizable object
• Eberhard Freitag
• effective topos
• Eilenberg-Moore category
• Eilenberg-Zilber category
• empty graph
• Ernst Cassirer
• Ernst Specker
• essential geometric morphism
• essential sublocale
• ETCC
• ETCS
• Euclidean geometry
• exact category
• exact square
• exponentiable functor
• exponentiable topos
• exponential object
• extensive category
• extremally disconnected topological space
• falling factorial
• fan theorem
• finite object
• finite set
• first-order theory
• flat functor
• flat modality
• forcing
• formalism
• formally étale morphism
• foundation of mathematics
• Fourier transform
• fracture theorem
• free cocompletion
• free monoid
• free topos
• Freyd cover
• Frobenius algebra
• Frobenius morphism
• Functorial Semantics of Algebraic Theories
• Gabriel–Ulmer duality
• Gaeta topos
• Galois connection
• Galois type
• generalized quantifier
• generalized Reedy category
• generic interval
• geometric theory
• geometry of physics -- supergeometry
• Gerhard Gentzen
• Gerhard Osius
• Giry monad
• Giuseppe Rosolini
• globe category
• globular set
• Gonzalo E. Reyes
• graph
• graphic category
• Gray tensor product
• Grothendieck fibration
• Grothendieck topos
• Grothendieck universe
• Grothendieck's Galois theory
• grouplike geometric morphism
• Hans Freudenthal
• Hartogs number
• Hegelian taco
• Hermann Cohen
• heteromorphism
• Higman's embedding theorem
• Hilbert space
• Hoàng Xuân Sính
• hypergraph
• hypermagma
• hyperring
• idempotent
• idempotent monad
• Ieke Moerdijk
• Immanuel Kant
• incompleteness theorem
• ind-object
• infinitary logic
• infinite judgement
• injective module
• injective object
• injective topos
• institution
• interior
• interval
• Isabelle
• Isar Stubbe
• Isbell duality
• Isbell envelope
• Jacques Penon
• Jason Parker
• Jean Bénabou
• Jean-Louis Verdier
• John Myhill
• John W. Gray
• Johnstone's topological topos
• Julie Bergner
• Jónsson-Tarski algebra
• Jónsson-Tarski topos
• Kan extension
• Kan lift
• Karl Rosenkranz
• Karoubi envelope
• Kazimierz Kuratowski
• Kimmo Rosenthal
• kinship
• Klaus Heiner Kamps
• Kleisli category
• Kripke-Joyal semantics
• Kurt Gödel
• language
• Laurent Lafforgue
• Lawvere distribution
• Lawvere theory
• Lawvere-Tierney topology
• lax-idempotent 2-monad
• left-determined model category
• level of a topos
• lex total category
• Lindström's theorem
• linear code
• linguistics
• linguistics - contents
• Loc
• locale
• localic geometric morphism
• localic topos
• locally closed set
• locally closed subtopos
• locally connected geometric morphism
• locally connected topos
• locally decidable topos
• Lou van den Dries
• Löwenheim-Skolem theorem
• Magari algebra
• manifold
• Marco Grandis
• Marcus Kracht
• Maria Manuel Clementino
• mathematics education
• measurable cardinal
• Mehrnoosh Sadrzadeh
• mereology
• Michel Coste
• mildly context-sensitive grammar
• minimal logic
• modal logic
• model theory
• moduli space
• monad (in computer science)
• monoidal category
• Montague semantics
• Mordell conjecture
• Morita equivalence
• Moritz Hauptmann
• motive
• motivic integration
• Moufang loop
• music theory
• Myles Tierney
• natural deduction
• natural homotopy
• natural numbers object
• negation
• Noam Chomsky
• Noether's theorem
• nuclear object
• Nullstellensatz
• number theory
• o-minimal structure
• objective number theory
• one-sided real number
• open geometric morphism
• open morphism
• Open problems in topos theory
• open subtopos
• opetopic omega-category
• Ore condition in a category
• over-topos
• Parmenides dialogue
• partial map classifier
• path category
• Patrick Dehornoy
• Paul Hertz
• Paul J. Cohen
• Peano arithmetic
• Per Lindström
• perfect space
• permutation model
• Peter Johnstone
• Platonism
• point of a topos
• pointed object
• predicate logic
• pregroup grammar
• pretopos
• profunctor
• projective plane
• projective space
• proof net
• propositions as types
• provability logic
• Puppe exact category
• pushout
• quality type
• quandle
• quasitopos
• quaternion
• quaternion group
• quaternionic set
• Quiv
• rack
• random variable
• rank
• real numbers object
• rectangular band
• Reedy model structure
• reflection principle
• reflexive object
• refutation by contradiction
• regular and exact completions
• regular category
• regular logic
• regular semicategory
• relation
• René Guitart
• René Thom
• Richard Garner
• Richard Montague
• Riemann surface
• rigid topology
• Robert Brandom
• Russell's paradox
• Salomon Maimon
• Sandbox
• scattered space
• scattered topos
• Schanuel topos
• Scott topology
• Scott topos
• second-order logic
• semi-abelian category
• semi-simplicial set
• semicartesian monoidal category
• semicategory
• semilinearity
• sequent calculus
• sheaf
• sheaf and topos theory
• Sierpinski topos
• sifted category
• skeletal geometric morphism
• sketch
• skew-simplicial set
• Skolem's paradox
• smooth manifold
• smooth structure on a topos
• Solomon Feferman
• stability in model theory
• Stephan Wannowski
• Stephen Houlgate
• Stephen Schanuel
• structuralism
• subobject classifier
• subtopos
• sufficiently cohesive topos
• surjective geometric morphism
• syllogism
• symmetric set
• symmetric topos
• syntax
• synthetic differential geometry
• tame topology
• test category
• theory of abelian groups
• theory of categories
• theory of decidable objects
• theory of flat functors
• theory of G-torsors
• theory of model homomorphisms
• theory of objects
• theory of presheaf type
• Theta category
• thick subcategory
• Thompson group
• topological site
• topos
• topos of pointed objects
• topos of recursive sets
• Topos Theory
• total category
• totally connected geometric morphism
• Tractatus Logico-Philosophicus
• transcendental grammar
• transcendental ideal
• transcendental syntax
• twisted arrow category
• two-valued logic
• two-valued topos
• type theory
• ultrafilter
• ultraproduct
• universe in a topos
• Uwe Petersen
• von Neumann regular category
• von Neumann–Bernays–Gödel set theory
• weakly open subtopos
• well-ordering theorem
• William Lawvere
• Wirthmüller context
• Yoneda lemma
• Yoneda structure
• ZFC
• étale geometric morphism
• étale map
• étendue
• Łoś ultraproduct theorem